Constructive heuristic replacement flow shop scheduling method

Abstract

The invention discloses a constructive heuristic replacement flow shop scheduling method, and belongs to the field of production scheduling. The method is used for solving the PFSP with the maximum completion time as the target, an initial scheduling sequence is obtained by constructing a mathematical programming model of the PFSP and descending according to the accumulated machining time of the workpieces, the workpieces are sequentially inserted into a local optimal scheduling sequence after the initial scheduling sequence is reduced, and the maximum completion time is obtained. And optimal local scheduling sequence selection is carried out based on the final completion time of the scheduling sequence on each machine. The method is mainly used for improving the flow shop production scheduling efficiency, reducing the production cost and improving the machine use efficiency.

Description

Technical Field

[0001] The invention belongs to the field of production scheduling, and in particular relates to a structural heuristic replacement flow shop scheduling method taking total completion time as an optimization target. Background Art

[0002] Permutation Flow-shop Scheduling Problem (PFSP) is a typical production scheduling problem in manufacturing and production systems, which is widely found in industrial production fields such as automobiles, metallurgy, petrochemicals, semiconductors, food and pharmaceuticals. It achieves the optimal goal of one or more goals of the entire production system by rationally arranging the processing sequence of workpieces and machines.

[0003] PFSP is a simplified model of many actual assembly line production scheduling problems and a typical NP-hard problem. Therefore, its research has important theoretical significance and engineering value. It is also the most widely studied type of classic scheduling problem. The solution methods of PFSP can be divided into two categories: exact algorithms and approximate methods according to the nature of the solution. Exact algorithms solve the optimal solution in the entire feasible domain of PFSP, mainly including branch and bound, Lagrangian relaxation, dynamic programming and other methods. However, due to the complexity of the permutation flow shop scheduling problem, the exact algorithm is only suitable for solving small-scale PFSP. The approximate method is to search for satisfactory solutions in the feasible scheduling space of PFSP, mainly including heuristic methods, meta-heuristic methods and artificial intelligence algorithms. Due to the efficient search performance and effect of approximate methods, they can generally be used to solve large-scale PFSP.

[0004] Among approximate methods, heuristic methods have been widely studied in academia due to their simple search structure, good search performance and transferability. In 1954, Johnson proposed the Johnson algorithm for solving the PFSP with two machines. In 1965, Palmer proposed the Palmer method for solving the general permutation flow shop scheduling problem, in 1969 Gupta proposed the Gupta method, in 1970 Campbell, Dudek and Smith proposed the Campbell-Dudek-Smith method (CDS), in 1983 Nawaz, Enscore, Ham proposed the Nawaz-Enscore-Ham method (NEH), etc.

[0005] The NEH method has become the focus of heuristic method research in recent years due to its high solution efficiency and has been considered one of the most efficient methods for solving PFSP. The basic idea of ​​the algorithm is to sort the processing time of jobs and gradually insert the jobs into the scheduling sequence to obtain a better scheduling solution. However, when the scale of the PFSP problem is large, the NEH method based on a single sorting rule will result in multiple workpieces and scheduling sequences being in the same sorting position, making it difficult to select the optimal workpiece and scheduling sequence from workpieces and scheduling sequences with the same sorting position. Summary of the invention

[0006] In order to overcome the shortcomings of the NEH method in solving PFSP, the present invention provides a constructive heuristic replacement flow shop scheduling method.

[0007] A structural heuristic replacement flow shop scheduling method of the present invention comprises the following steps:

[0008] Step 1: Establish the PFSP mathematical model.

[0009] Let n represent the number of workpieces, m represent the number of machines, J = {1,2,…,i,…,n} represents the set of workpieces, M = {1,2,…,j,…,m} represents the set of machines, and p i,j , i∈J, j∈M represents the processing time of the i-th workpiece on the j-th machine, C i,j , i∈J, j∈M represents the completion time of the i-th job on the j-th machine. Let π={π1,…,π i ,,…,π n},π i ∈J represents a processing sequence of all workpieces, C max represents the maximum completion time, then

[0010] 1) Optimization objectives:

[0011] minC max #(1)

[0012] 2) Constraints:

[0013]

[0014] 3) Decision variables

[0015] π=perm({1,2,…,i,…,n})#(7)

[0016] Where: Formula (1) indicates that the decision objective of scheduling is to minimize the maximum completion time, and Formula (7) indicates that the scheduling scheme π is a permutation sequence of the job set J = {1, 2, …, i, …, n}.

[0017] Step 2: Calculate the cumulative processing time of each workpiece on each machine in turn

[0018]

[0019] Each workpiece is divided into m >s m-1 >…>s 1 The priority is sorted in descending order, and the initial sequence π={π1,…,π n}.

[0020] Step 3: Initialize the local scheduling sequence π′={π1}, the local sequence to be scheduled π″={π2,…,π n}; define k=1.

[0021] Step 4: Select the current local sequence to be scheduled π″={π k+1 ,…,π n}'s first workpiece π k+1 Insert the current local scheduling sequence π′={π′1,…,π′ k}, we get the current local insertion scheduling sequence set Π = {π 1 ,…,π k+1}.

[0022] Step 5: Calculate each local insertion scheduling sequence {π 1 ,…,π k+1 Final completion time on each machine ,l=1,…,k+1;j∈M, each local insertion scheduling sequence follows C m >C m-1 >…>C 1 The priority is sorted in ascending order to obtain the optimal local insertion scheduling sequence π″′={π″′1,…,π″′ k+1}.

[0023] Step 6: Update the current local scheduling sequence π′=π″′, the local sequence to be scheduled π″={π k+2 ,…,π n}.

[0024] Step 7: If the local sequence to be scheduled is an empty set, the optimal scheduling sequence π′ is obtained; otherwise, k=k+1, and return to step 4.

[0025] The beneficial effects of the present invention are: using multi-dimensional priorities for sorting, reducing the randomness of the initial sequence and the local insertion scheduling sequence, and obtaining a better final scheduling solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 The example results of the present invention are shown in FIG. DETAILED DESCRIPTION

[0027] The specific implementation modes of the present invention are further described below with reference to the accompanying drawings and specific examples.

[0028] A structural heuristic replacement flow shop scheduling method of the present invention comprises the following steps:

[0029] Step 1: Establish the PFSP mathematical model.

[0030] Take the PFSP with 4 workpieces and 3 machines as an example. The workpieces are processed on each machine in turn. The processing time is shown in the following table:

[0031]

[0032] PFSP satisfies the following requirements: (1) All workpieces can be processed at time zero; (2) Each machine can process only one workpiece at a time; (3) Each machine is interrupted once it starts processing; (4) The buffer between machines is infinite; and (5) The goal is to minimize the maximum completion time.

[0033] Then the number of workpieces n = 4, the number of machines m = 5, the set of workpieces J = {1,2,3,4}, the set of machines M = {1,2,3}, and the processing time is p i,j ,i∈J,j∈M, the completion time is C i,j , i∈J, j∈M, the processing sequence is π={π1,…,π i ,,…,π n},π i ∈J, the maximum completion time is C max .

[0034] 1) Optimization objectives:

[0035] minC max

[0036] 2) Constraints:

[0037]

[0038]

[0039] 3) Decision variables

[0040] π=perm({1,2,3,4})

[0041] Step 2: Calculate the cumulative processing time of each workpiece on each machine in turn, sort them in descending order according to the priority of the cumulative processing time, and obtain the initial sequence.

[0042] The cumulative processing time of workpiece 1 on each machine:

[0043]

[0044] The cumulative processing time of workpiece 2 is {83, 86, 175}, the cumulative processing time of workpiece 3 is {15, 26, 75}, and the cumulative processing time of workpiece 4 is {71, 127, 216}. The initial sequence π is obtained by sorting.

[0045] Step 3: Initialize the local scheduling sequence and the local sequence to be scheduled.

[0046] When k=1, the local scheduling sequence is π′={4}, and the local sequence to be scheduled is π″={2,1,3}.

[0047] Step 4: Select the first workpiece of the current local sequence to be scheduled and insert it into all possible positions of the current local scheduling sequence to obtain the current local insertion scheduling sequence set.

[0048] When k = 1, the first workpiece of the current local to-be-scheduled sequence π″ = {2, 1, 3} is workpiece 2, and the current local insertion scheduling sequence set Π = {π 1 ,π 2}, π 1 ={2,4} and π 1 ={4,2}.

[0049] Step 5: Calculate the final completion time of each local insertion scheduling sequence on each machine, sort each local insertion scheduling sequence in ascending order according to priority, and obtain the optimal local insertion scheduling sequence.

[0050] When k = 1, the local insertion scheduling sequence π 1 ={2,4}The final completion time on each machine:

[0051]

[0052]

[0053] Local insertion scheduling sequence π 2 ={4,2} The final completion time on each machine is {154,210,305}. Then the optimal local insertion scheduling sequence π″′={2,4}.

[0054] Step 6: Update the current local scheduling sequence and the local sequence to be scheduled.

[0055] When k=1, the current local scheduling sequence is π′={2,4}, and the local sequence to be scheduled is π″={1,3}.

[0056] Step 7: Since the current local sequence to be scheduled is π″={1,3} which is not an empty set, k=2, return to step 4. The current local sequence to be scheduled in each stage can be obtained in sequence as {1,2,4} and {3,1,2,4}. Then the optimal schedule is {3,1,2,4}, and the maximum completion time is 337. The scheduling plan is as follows Figure 1 shown.

Claims

1. A constructive heuristic permutation flow shop scheduling method, characterized in that: The following steps are involved: Step 1: Establish the PFSP mathematical model. Let n represent the number of workpieces, m represent the number of machines, J = {1,2,…,i,…,n} represents the set of workpieces, M = {1,2,…,j,…,m} represents the set of machines, and p i,j , i∈J, j∈M represents the processing time of the i-th workpiece on the j-th machine, C i,j , i∈J, j∈M represents the completion time of the i-th job on the j-th machine. Let π={π1,…,π i ,,…,π n },π i ∈J represents a processing sequence of all workpieces, C max represents the maximum completion time, then 1) Optimization objectives: minC max #(1) 2) Constraints: 3) Decision variables π=perm({1,2,…,i,…,n})#(7) Where: Formula (1) indicates that the decision objective of scheduling is to minimize the maximum completion time, and Formula (7) indicates that the scheduling scheme π is a permutation sequence of the job set J = {1, 2, …, i, …, n}. Step 2: Calculate the cumulative processing time of each workpiece on each machine in turn Each workpiece is divided into m >s m-1 >…>s 1 The priority is sorted in descending order, and the initial sequence π={π1,…,π n }. Step 3: Initialize the local scheduling sequence π′={π1}, the local sequence to be scheduled π″={π2,…,π n }; define k=1. Step 4: Select the current local sequence to be scheduled π″={π k+1 ,…,π n }'s first workpiece π k+1 Insert the current local scheduling sequence π′={π′1,…,π′ k }, we get the current local insertion scheduling sequence set Π = {π 1 ,…,π k+1 }. Step 5: Calculate each local insertion scheduling sequence {π 1 ,…,π k+1 Final completion time on each machine ,l=1,…,k+1;j∈M, each local insertion scheduling sequence follows C m >C m-1 >…>C 1 The priority is sorted in ascending order to obtain the optimal local insertion scheduling sequence π″′={π″′1,…,π″′ k+1 }. Step 6: Update the current local scheduling sequence π′=π″′, the local sequence to be scheduled π″={π k+2 ,…,π n }. Step 7: If the local sequence to be scheduled is an empty set, the optimal scheduling sequence π′ is obtained; otherwise, k=k+1, and return to step 4.

2. A constructive heuristic replacement flow shop scheduling method according to claim 1, characterized in that: In step 5, the scheduling sequence π is locally inserted l Final completion time The calculation method is: Denote π l ={π1,…,π n}, then

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